LJ-60 CREW POSSIBLY SHUT DOWN THE WRONG MALFUNCTIONING ENG.

Narrative

POSITIONED FLT FROM KISSIMMEE (ISM) TO CHARLESTON (CHS). CLBING OUT OF ISM; WERE GIVEN INTERMEDIATE CLB FROM 4000 FT MSL TO 7000 FT. I WAS ACTING AS SIC AND PF. THE AIRSPD WAS 200 KTS AND AS WE WERE GIVEN A CLB FROM 4000 FT TO 7000 FT; INITIALLY THE ACFT STARTED SHAKING AND WE HEARD 3-4 LOUD BANGS. THE ACFT YAWED BACK AND FORTH AND ENG INDICATIONS WERE NORMAL; OTHER THAN N1 ON R-HAND (#2) ENG THAT FLUCTUATED BTWN 90-98% BACK AND FORTH. AFTER TKOF CHK HAD BEEN COMPLETED PRIOR TO THE EVENT; AND THE AUTOMATIC PWR REDUCTION WAS OFF. AFTER EVALUATING SIT; RETARDING BOTH THROTTLES; WE SMELLED SOMETHING BURNING. WITH THE ENGS BACK; WE ELECTED TO GET R-HAND ENG BACK TO IDLE. NO LIGHTS ON ANNUNCIATOR PANEL ILLUMINATED. THE BURNING SMELL PERSISTED AND WE ELECTED TO SHUT DOWN R-HAND (#2) ENG. L ENG GAUGES INDICATED NORMAL READINGS FOR SELECTED PWR SETTINGS. WE SECURED THE R-HAND ENG WITH APPROPRIATE EMER CHKLISTS AND PROCEEDED TO A NORMAL LNDG. AN EMER WAS DECLARED BY THE PIC (PNF) AND THE EMER EQUIP ROLLED ONTO THE RAMP. AFTER A NORMAL LNDG; WE PROCEEDED TO EXIT THE RWY AND SHORTLY AFTER; WE GOT A L-HAND ENG VIBRATION LIGHT AND L-HAND ENG OIL PRESSURE LIGHT ON ANNUNCIATOR ILLUMINATED. WE SHUT DOWN THE L-HAND ENG AND WERE SUBSEQUENTLY TOWED BACK TO THE FBO RAMP.